The prior art TFT semiconductor device has used a heatproof insulating substrate made of quartz or the like. TFTs have been fabricated at a high density by performing a high-temperature process above 1000.degree. C. Such TFT semiconductor devices have been earnestly developed, for example, as active matrix array substrates for active matrix liquid crystal displays. To find wider application of liquid crystal displays, there is a demand for a reduction in cost of fabricating TFT semiconductor devices. Low-temperature processes capable of adopting cheaper glass substrates have been discussed. Especially, in order to fabricate a large-sized, high-information content liquid crystal display, low-temperature processes capable of utilizing cheaper glass substrates have been earnestly developed. In this connection, a technique consisting of forming a film of amorphous silicon on a glass substrate of a relatively low melting point and irradiating the film with a laser beam to convert the film into high-quality polysilicon has been studied. Since polysilicon has larger carrier mobility than that of amorphous silicon, high-performance TFTs can be formed at a high density.
Amorphous silicon is once melted by laser irradiation and then becomes polycrystalline. In the prior art techniques, when amorphous silicon is changed into a polycrystalline state by laser annealing in this way, the original amorphous silicon thin film is formed to a thickness of 40 to 50 nm or to a thickness of about 100 nm. If laser annealing is performed with such thicknesses, the crystals are epitaxially grown in the direction of thickness of the thin film. Therefore, the crystal grain sizes are increased by amounts corresponding to the thickness of the film. However, where an amorphous silicon thin film has a thickness of 40 to 50 nm or more, individual crystal grains tend to be grown in the direction of the thickness, i.e., in the vertical direction. Furthermore, the grain sizes of silicon crystals formed by laser annealing depend heavily on the intensity, or energy, of the irradiating laser radiation. For these reasons, if the uniformity of the cross-sectional energy distribution of the laser beam is poor, then it follows that the crystal grain sizes of silicon are not uniform. Moreover, the silicon crystal grain size at the interface between non-irradiated and irradiated regions differs from the crystal grain size in the center of the irradiated region. Once silicon crystals of small grain sizes are formed by laser annealing with a relatively small energy, if the crystals are subsequently irradiated with laser beam having a relatively large energy, then it is very difficult to increase the crystal grain sizes up to the level achieved by the method consisting of first irradiating crystals with laser beam of relatively large energy so as to grow the crystals to large sizes. Consequently, crystal grains once grown are not greatly grown even if laser annealing is again performed and so it is difficult to modify the grain sizes. Where amorphous silicon is changed into polycrystalline silicon, the amorphous silicon is sometimes scanned with laser beam of a given cross-sectional area such that one irradiated region overlaps with the adjacent irradiated region. In this way, an amorphous silicon thin film of a large area can be changed into a polycrystalline silicon thin film. In this case, if the thickness of the amorphous silicon thin film is in excess of 40 nm, it has been difficult to perform laser annealing in such a way that crystal grain sizes are increased uniformly. For example, the continuity of the crystal grain size is disturbed at the interface between the adjacent irradiated regions overlapping with each other.